Abstract
Sub-Jupiter classed circumbinary planets discovered in close-in binary systems have orbits just beyond the dynamically unstable region, which is determined by the eccentricity and mass ratio of the host binary stars. These planets are assumed to have formed beyond the snow line and migrated to the current orbits rather than forming in situ. We propose a scenario in which a planet formed beyond the snow line and migrated to the inner edge of the circumbinary disk, which was within the unstable area, and then moved to the current orbit through outward transportation. This outward transportation is driven by the balance of orbital excitation of the central stars inside the gravitationally unstable region and damping by the gas-drag force. We carried out N-body simulations with a dissipating circumbinary protoplanetary disk for binary systems with different eccentricities and mass ratios. Planets are more likely to achieve a stable orbit just beyond the unstable region in less eccentric binary systems. This result is not as sensitive to mass ratio as it is to eccentricity. These dependencies are consistent with the data from observed binary systems hosting circumbinary planets. We find CBPs’ orbits close to the instability boundaries are explained by our orbital evolution scenario.
Highlights
IntroductionThe Kepler satellite has discovered many close-in circumbinary planets (CBPs), namely Kepler-16b (Doyle et al 2011), Kepler-34b (Welsh et al 2012), Kepler-35b (Welsh et al 2012), Kepler-38b (Orosz et al 2012b), Kepler-47b, Kepler-47c (Orosz et al 2012a, 2019), Kepler-47d (Orosz et al 2019) PH1(Kepler-64b) (Schwamb et al 2013), Kepler-413b (Kostov et al 2014), Kepler-453b (Welsh et al 2015), and Kepler-1647b (Kostov et al 2016)
In the disk of surface density fdisk ≤ 0.316, the planet’s semi-major axis oscillates just over the unstable boundary with small amplitude. This is due to the weak negative torque by the weak gas-drag force in these low-density disks and weak orbital excitation because of large planet’s orbital distance, which is outside the unstable area
Our results suggest that circumbinary planets (CBPs)’ orbits just over the instability boundary can be achieved via our transportation scenario even if the planets once entered the unstable area
Summary
The Kepler satellite has discovered many close-in circumbinary planets (CBPs), namely Kepler-16b (Doyle et al 2011), Kepler-34b (Welsh et al 2012), Kepler-35b (Welsh et al 2012), Kepler-38b (Orosz et al 2012b), Kepler-47b, Kepler-47c (Orosz et al 2012a, 2019), Kepler-47d (Orosz et al 2019) PH1(Kepler-64b) (Schwamb et al 2013), Kepler-413b (Kostov et al 2014), Kepler-453b (Welsh et al 2015), and Kepler-1647b (Kostov et al 2016). The spectral types of the binary host stars are KM (Kepler-16, -413), GG (Kepler-34, -35, -1647), GM (Kepler-38), and FM (Kepler-64). Their masses are ∼ 1M⊙ , the primary and secondary stars are separated by ∼ 0.2 au, and the orbital eccentricities are ∼ 0.1 except for the Kepler-34 and PH1 When a planet enters within a certain semi-major axis, its orbit experiences strong excitation by the time-varying gravitational potential, leading to the orbital instability. In Quarles et al (2018), the sizes of this unstable region for co-planar orbits were derived by N-body simulations as a function of the binary eccentricity and mass ratio, Yamanaka and Sasaki Earth, Planets and Space (2019) 71:82
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